Question

The vertex of this parabola is at (-3, -2). Which of the following could be its

equation?
-5
(-3,-2)
5
-5
O A. y=-2(x-3)² + 2
OB. y=-2(x-3)²-2
O C. y=-2(x+3)² + 2
D. y = -2(x+3)²-2
5
X

Answer 1

The equation of a parabola in vertex form is given by y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.

Explanation:

Given that the vertex of the parabola is (-3, -2), we can substitute these values into the equation:

y = a(x - (-3))^2 + (-2)

y = a(x + 3)^2 - 2

Now, let's analyze the given options:

A. y = -2(x - 3)^2 + 2

This equation does not match the given vertex coordinates. The vertex is at (-3, -2), not (3, 2).

B. y = -2(x - 3)^2 - 2

This equation matches the given vertex coordinates. The vertex is at (-3, -2).

C. y = -2(x + 3)^2 + 2

This equation does not match the given vertex coordinates. The vertex is at (-3, -2), not (-3, 2).

D. y = -2(x + 3)^2 - 2

This equation does not match the given vertex coordinates. The vertex is at (-3, -2), not (-3, -4).

Therefore, the equation that could represent the parabola with a vertex at (-3, -2) is:

B. y = -2(x - 3)^2 - 2